Can I override the ATMega32u4 on the Leonardo, and program an ATMega328?

I want to get a new Arduino Leonardo, but I usually make standalone Arduinos with the ATMega328. Is there some way to override the ATMega32u4 on the Leonardo, and program an ATMega328?

I don't think I understand what you mean. You want to get a Leonardo, but you don't want to use its processor?

Why override? Load the Arduino as bootloader sketch into the Leonardo, let it bootload the 328.

Otherwise no, the SPI pins are not controlled without the Leonardo chip to do something for you.

I'd recommend adding a tool to your bag of tricks: a simple AVR ISP such as this
http://www.mdfly.com/index.php?main_page=product_info&cPath=5_6&products_id=415
or one of the equivalent programmers.

Or learn to use the ArduinoISP sketch and use your Leaonardo to program/bootload the chips.